Variational wavefunctions for Sachdev-Ye-Kitaev models

TL;DR

This paper introduces a new class of variational wavefunctions inspired by coupled cluster methods for SYK models, demonstrating they achieve a significant energy approximation and capture symmetry breaking.

Contribution

The authors propose a novel variational wavefunction approach for SYK models, overcoming limitations of Gaussian states, and develop a static large-N field theory to analyze their properties.

Findings

Achieve an approximate energy ratio of 0.62 to the ground state for q=4 SYK.

Provide an exact description of spontaneous symmetry breaking in a related SYK model.

Demonstrate the failure of Gaussian states in fermionic SYK models.

Abstract

Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wavefunctions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static ("0+0D") large-$N$ field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of $r \approx 0.62$ between the variational and ground state energy of SYK for $q=4$. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.